MATH M118 Lecture Notes - Lecture 2: Sample Space
17 Sep 2016
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Document Summary
Simply put, combinatorics is the mathematics of counting finding out how many ways an. There are many experiments for which it is fairly easy to count all of the possible outcomes. However, some experiments have far too many outcomes to count by hand. In this chapter, we will explore various methods for calculating how many ways an experiment can be done. The set of all possible outcomes is called the sample space, denoted by s. So, for the previous examples of flipping a coin and rolling a die we would have: Flipping a coin: s = {h,t} and n(s) = 2. Rolling a die: s = {1,2,3,4,5,6} and n(s) = 6. S = {(1,1), (1,2), (1,3) (6,6)} n(s) = 36. Each act of an experiment is called a stage. The experiments above have only one stage to them. We will explore methods in this chapter for finding the cardinality of a sample space from a multi-stage experiment.
